A Numerical Study of Some Hessian Recovery Techniques on Isotropic and Anisotropic Meshes

Authors:
Marco Picasso;Frédéric Alauzet;Houman Borouchaki;Paul-Louis George
Affiliations:
marco.picasso@epfl.ch;Frederic.alauzet@inria.fr and paul-louis.george@inria.fr;houman.borouchaki@utt.fr;-
Venue:
SIAM Journal on Scientific Computing
Year:
2011

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Abstract

Spaces of continuous piecewise linear finite elements are considered to solve a Poisson problem, and several numerical methods are investigated to recover second derivatives. Numerical results on 2D and 3D isotropic and anisotropic meshes indicate that the quality of the results is strongly linked to the mesh topology and that no convergence can be insured in general.